Interaction between Dirac fermions and phonons on the (001) surface of the strong 3D topological insulator Bi$_2$Te$_3$

We report on studies of the interaction of Dirac fermion quasiparticles with phonons on the (001) surface of the strong 3D topological insulator Bi$_2$Te$_3$. Studying this coupling is essential for determining the technological viability of this new class of materials. We employed inelastic helium atom scattering to determine surface phonon dispersions along the $\Gamma$M and $\Gamma$KM directions. In contrast to our previous studies on Bi$_2$Se$_3$,\footnote{Zhu, et al. Phys. Rev. Lett. 107, 186102, 2011.} which exhibited a strong Kohn anomaly at $2k_F \approx 0.2$\AA$^{-1}$ in a low-lying optical phonon branch, the current results show a weaker Kohn anomaly at $2k_F \approx 0.1$\AA$^{-1}$ in a similarly low-lying branch. The lower value of $k_F$ is consistent with the smaller carrier concentration in Bi$_2$Te$_3$ as evidenced by Hall conductivity measurements. Our results are further substantiated by lattice dynamical calculations performed within the pseudo-charge model. We also report on a detailed analysis of the electron-phonon coupling as a function of phonon branch index and wave vector utilizing the methods we recently developed.\footnote{Zhu, et al. Phys. Rev. Lett. 108, 185501, 2012. }